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Introduction to Statistics and Probability

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  • September 3, 2021

Statistics and Probability

We are all aware of the importance of statistics and probability in our lives. This is something we’ve been learning in school and even in college. In this article, we’ll go over the basics/fundamentals of statistics, as well as their relevance, real-world applications, and job opportunities in the area.


Statistics is a discipline of applied mathematics that deals with gathering, describing, analyzing, and finding conclusions from numerical data. Mathematical analysis, linear algebra, and differential equations are some of the mathematical tools used in various research. This enables one to understand multiple results from it. It also enables one to predict a variety of possible outcomes for different situations.

Stats are numerical numbers that represent information, observations, and data. With the help of statistics, we can find numerous indications of central tendencies. We can also find the divergence of various values from the center. Statisticians are mainly interested in learning how to draw valid conclusions about huge groups and general events from the observable characteristics of small samples. Data from observational studies is collected using sample survey methods. These small samples reflect a subset of a larger group.

The following are some examples of common statistical tools and procedures:

  • Descriptive
  • Mean (average)
  • Null hypothesis testing
  • Linear regression analysis
  • Analysis of variance (ANOVA)
  • Logit/Probit models
  • Variance
  • Skewness
  • Kurtosis
  • Inferential


The following are the uses of statistics:

  • It helps in the collection of proper quantitative data.
  • It helps in the presentation of complicated data in a tabular, or visual format. This is for easy and consistent understanding.
  • It also assists in explaining the nature and pattern of variability through quantitative observations.

Stages of Statistical Analysis

  • Collecting: Firstly, data will be extracted from various sources. It is the first stage in statistical analysis. This extraction is done in a variety of ways depending on the situation.
  • Arranging: The second stage is to arrange the information in a meaningful way so that the information is easy to comprehend.
  • Presenting: The third stage is all about simplifying the information. Presentations can make results more interesting and engaging in the form of diagrams, charts, and so on. Likewise, they help in demonstrating correlations between facts.
  • Analyzing: The fourth stage is to obtain the desired outcomes. This stage frequently uses measures of central tendency, measures of dispersion, regression, correlation, and interpolation.
  • Interpreting: The final stage is to analyze the data in order to make forecasts. Furthermore, interpretation deals with data rendering and data assessment. It is concerned with the outcome supported by mathematical reasoning and pre-planned standard methods.

Types of Statistics

It can be divided into two categories:

  1. Descriptive
  2. Inferential


The central tendency, variability, and distribution of sample data are the subject of descriptive statistics. The typical aspects of a sample or population are the approximate features of central tendency. The central tendency includes descriptive statistics such as mean, median, and mode. Variability, on the other hand, is a collection of statistics. It shows how much difference exists among the constituents of a sample or population.

A sample data distribution is the general pattern of the data on a graph such as a histogram. Some features which a sample data distribution contains are probability distribution function, kurtosis, and skewness. Descriptive statistics help in presenting variations in the characteristics of data set components. Ultimately, it helps to understand the collective features of the components in a data sample, as well as to make decisions using inferential statistics.

Methods of Descriptive Statistics

  • Tabular Methods: A frequency distribution is the most popular tabular method of data for a single variable. It represents the amount of data values in each of many discrete groups. A relative frequency distribution is a tabular method that illustrates the percentage of data values in each class. Whereas, a cross-tabulation is a two-variable version of a frequency distribution. It is the most basic tabular presentation of data for two variables. On the other hand, a frequency distribution for a qualitative variable displays the number of data values in each qualitative category. For example, the gender variable has two alternatives which are male and female. As a result, a frequency distribution for gender would indicate the number of males and females in two discrete groups.
  • Graphical Methods: A variety of graphical approaches for expressing information exist, such as a bar graph and a histogram. A frequency distribution helps a bar graph in graphically representing qualitative data. The graph’s horizontal axis displays labels for the qualitative variable’s categories. However, above each label is a bar. Each bar is at a height which corresponds to the number of data values in the category. The most popular graphical representation of quantitative data presented in a frequency distribution is a histogram.


Interpreting the meaning of descriptive statistics is the focus of inferential statistics. Inferential Statistics explains the meaning of the gathered information after obtaining, processing, and summing up the information. They help in testing hypotheses and in finding connections between variables. They also assist in predicting population size. Not only that, but inferential statistics also help to make meaningful generalizations from samples by drawing findings and inferences.

Regression Analysis

Regression analysis determines the degree and type of the link (i.e., the correlation) between a dependent variable and one or more independent variables. It is a popular statistical inference method. A regression model is a result of hypothesizing a relationship model and approximating parameter values to generate an estimated regression equation. Eventually, the model goes through a series of tests to determine its suitability. If the model proves to be satisfactory, the computed regression equation helps in predicting the value of the dependent variable given values for the independent variables.

Real-World Applications

Some instances of real-world statistics applications are as follows:

  • Statistical Modeling: Statistical modeling includes creating predictive models based on information development, pattern recognition, and design. Political outcome predictions, population survival analysis, and scientific surveys require modeling. Forecasters make use of these technologies to predict the weather and investigate various environmental and geographical disturbances on the planet.
  • Government Sector: Government decisions are generally the result of well-researched information and figures. Their decisions have an impact on areas of health, education, population, and development.
  • Business: Every type of organization has a statistical research section which help them in predicting and analyzing the company’s present and projected growth. A firm’s success is dependent on recognizing what is essential. Statistics, in short, can help the business in doing so.
  • Sports: If you read my previous article on Sports Analytics, you already know how crucial statistical analysis is in the sports industry. Statistical analysis is essential to improve the efficacy of any sport. For instance, it aids a sportsperson in better understanding his or her performance in a certain sport.
  • Psychology: Psychology is the study of the brain and is a combination of science and medicine. Statistics help in analyzing human behaviour and in anticipating thoughts and behaviours that could occur in the future.
  • Weather Forecasting: Statistics play a big role in weather forecasting. Computer-based weather forecasting is based on a set of statistical functions. Finally, all of these figures result in comparing the current weather to past weather conditions.
  • Diseases Prediction: We can use statistics to figure out how many individuals are impacted by a particular illness. It also shows how many individuals have died as a consequence of the same illness.

Career Scope and Salary in the field of Statistics

From our discovery, we realize how statistics has an effect in a wide range of fields, including business, agriculture, industry, government, computer science, health sciences, and various other fields. Students can work in financial services, software development, analytics, actuarial science, and a number of other professions after earning their bachelor’s degree. Not only that, but after finishing their statistics degree, students can also apply for the Civil Services, Indian Statistical Services, and Indian Economic Services tests.

According to Glassdoor, the average annual pay in India for a statistician is Rs. 4,09,615. The highest annual salary for a statistician in India is Rs. 20,13,808 per year, while the lowest annual pay for a statistician is Rs. 2,61,400.

According to LeverageEdu, Given below are some potential job titles and top recruiters for someone having a background in statistics.

Job Titles

The following are the job titles:

  • Statistician
  • Mathematician
  • Business Analyst
  • Data Scientist
  • Data Analyst
  • Atmospheric Scientist/Meteorologist
  • Risk Analyst
  • Sports Data Analyst
  • Content Analyst
  • Biostatistician
  • Econometrician
  • Market Research Analyst.
  • Research Analyst
  • Professor
  • Operations Research Analyst
  • Financial Analyst
  • Consultant

Top Recruiters

The following are the top recruiters:

  • Blue Ocean Marketing
  • TCS Innovations Labs
  • HP
  • Accenture
  • HSBC
  • HDFC
  • Deloitte Consulting
  • Nielsen Company
  • American Express
  • Genpact
  • GE Capital